Bootstrapping and infinite regress... that reminds me of this branch of logic: https://en.wikipedia.org/wiki/Infinitary_logic https://en.wikipedia.org/wiki/Inf

Bootstrapping and infinite regress... that reminds me of this branch of logic: https://en.wikipedia.org/wiki/Infinitary_logic https://en.wikipedia.org/wiki/Infinitary_logic with which you can prove a theorem by assuming it in the first place, using infinitary (or circular) proofs and an algorithm to transform these proofs into usual proofs.